The paper machine is a large-scale process to convert fibers into sheets of paper with high efficiency. It has hundreds of actuators at the head along the cross direction to control the properties of the pulp on the paper sheet. Thousands of measurement boxes are located at the end to measure the paper properties. For the controller design, there are two important directions associated with the paper machine: machine direction (MD) and cross direction (CD). The MD refers to the direction in which the paper sheet moves while the CD is the direction perpendicular to the MD.
Apart from the large number of actuators and measurement bins, the CD process is also an ill-conditioned process. Besides, the CD process model suffers from large uncertainties. All of these characteristics add to the complexity associated with the corresponding model identification and controller design. A common technique to address this issue assumes that all the actuators have identical temporal (in the time direction) and spatial (in the CD) response behavior. Moreover, the temporal and spatial responses are assumed to be separable. These assumptions are valid in practice and make the CD process easier to handle. Even then, the controller design and model identification for the CD process are still challenging.
A current control employed in the CD process is model predictive control (MPC) that requires a model with good quality. Therefore, model identification for the CD process plays an essential role in determining the performance of the MPC. In terms of the system identification, it is well known that a good excitation signal is necessary to make the identified model reliable and precise. How to design the excitation signal in an optimal way has received extensive attention. A number of well-known strategies have been proposed such as the frequency domain approach, time domain approach, open-loop optimal input design and closed-loop optimal input design.
In terms of the optimal input design for the CD process, most existing results focus on the open-loop case to generate good data for process model identification, which risks interrupting normal process operations and sacrificing quality. The main drawback is that it may bring significant profit loss for the mills as the normal operations are interrupted. The industry needs a technique that can generate good quality process data without having to suspend control and without sacrificing product quality.